Combinations of events. Opposite events

Sum and product of events

Product

A\cdot B

(or

A\cap B

) — the event “both occurred:

A

and

B

”. Sum

A+B

(often

A\cup B

) — the event “at least one of

A, B

occurred” (including both simultaneously when possible). Events are mutually exclusive if $A\cap B=\varnothing$ : in one trial they cannot** both occur.

Textbooks may differ slightly in notation (

\cdot

\cap

) — the meaning is the same

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